### RD Sharma Class 10 Solutions Chapter 9 Arithmetic Progressions Ex 9.3 Q14

### Ex 9.3 Q14.

An arithmetic progression is a sequence of numbers in which each number is the sum of the previous two. In other words, a sequence of numbers in which the difference between any two consecutive numbers is constant.

For example, the numbers 1, 2, 3, 4, 5 form an arithmetic progression with a difference of 1 between consecutive terms.

The first few terms of an arithmetic progression are:

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50.

There are a few properties of arithmetic progressions that are worth mentioning.

The sum of the first n terms of an arithmetic progression is given by the formula:

Sn = a + (n-1)d

Where a is the first term of the sequence, d is the difference between consecutive terms, and n is the number of terms in the sequence.

For example, the sum of the first 10 terms of the sequence 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 is 55.

Another property of arithmetic progressions is that the product of the first n terms is given by the formula:

An = a(1 + (n-1)d)

Where a is the first term of the sequence, d is the difference between consecutive terms, and n is the number of terms in the sequence.

For example, the product of the first 10 terms of the sequence 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 is 1000.